The study, based on in-depth interviews with chief executives in voluntary organisations, finds real concern among leaders that younger senior managers are not being developed.
One chief executive remarked: "The sector must start recruiting and grooming new blood at the post-graduate stage, not wait for old has-beens who move into the voluntary sector because they've got fed up with the bureaucracy of the public sector."
The report, Leadership in Voluntary-Sector Organisations, was presented at a debate organised by ACEVO last week on the role of charity chief executives.
The report's author Stephen Bevan, deputy director of research at the Work Foundation, said: "There is a succession time bomb ticking away in the third sector. With all the changes, complexity and pressures faced by chief executives, many voluntary-sector leaders face a crisis of succession, with few talented visionary leaders queuing up to take on what has become one of the most challenging leadership roles in the UK."
Bevan blamed a lack of structured leadership development in the sector "to ensure that the next cadre of chief executives is coming through the system".
He said that already more chief executives posts were being filled from outside the sector and "in five years it could be a lot worse".
The reports also highlights the considerable uncertainty among chief executives over the increasing trend towards mergers and takeovers prompted by difficulties in accessing funding.
One chief executive from a homelessness charity commented: "You can see the chief executives in their planning are thinking about whether they're going to be taken over. In one way it's making people very competitive, on the other level, it's making people very accessible in a friendly way."
Chief executives also predicted more difficulties in recruiting and retaining senior staff. "Recruitment and retention is one of the big issues facing the sector because salaries are still relatively low. (A senior member of staff) knows she can get more money doing probably a job with less stress and less responsibility in the corporate sector with her skills," said one chief executive.
So-called "pull factors" which had to be nurtured in order to attract staff include input into the decision-making process, the sense of making a difference, training and development opportunities and promotion prospects.